From the waist up, Liza Minnelli jokes tonight, she's "Dorothy's daughter", but from the waist down, her hip and knee replacements make her "the Tin Man's kid". Rueful self-mockery is a key element of the Minnelli brand – though "brand" is inappropriately modern lingo for a star whose bosom pals included the man she calls "Uncle Frank" (Sinatra to you and me).

Now 65, Minnelli is one of the last links to Sinatra's era, and in her show she plays on her status as a conduit to the past. She herself has never quite left it behind; her set is mainly drawn from the heyday of cabaret (both upper- and lower-case "c"), going back as far as Alexander's Ragtime Band. Each song is preceded with wisecracking anecdotage about Uncle Frank or Gwen Verdon or some other golden-age luminary, illustrating the point that Minnelli is the last of a breed.

Aptly, the setlist is packed with songs rarely heard this century: Peggy Lee's He's a Tramp, her own Liza With a Z, and Charles Aznavour's prescient gay anthem What Makes a Man, delivered with maximum quivering drama.

Her physical frailty has almost been incorporated into the act: when singing leaves her breathless and parched she makes a joke about needing water, and once or twice plops into a chair with visible relief. It's not always easy to watch, and when she pauses to summon stamina before slamming home the climaxes of Cabaret and New York, New York, all guns just about blazing, it's not easy to listen. But the harder she works, the more encouraging the applause, and the fans' love is obviously a lifeline. "I'll never forget this for as long as I live," she says, and it has the ring of sincerity.